caa a22 4500 445868996 CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00605-009-0161-8 doi (NATIONALLICENCE)springer-10.1007/s00605-009-0161-8 Müller Wolfgang Institut für Statistik, Technische Universität Graz, 8010, Graz, Austria aut On the value distribution of positive definite quadratic forms [Elektronische Daten] [Wolfgang Müller] Denote by 0=λ 0<λ 1≤λ 2≤. . . the infinite sequence given by the values of a positive definite irrational quadratic form in k variables at integer points. For l≥ 2 and an (l −1)-dimensional interval I=I 2×. . .×I l we consider the l-level correlation function $${K^{(l)}_I(R)}$$ which counts the number of tuples (i 1, . . . , i l) such that $${\lambda_{i_1},\ldots,\lambda_{i_l}\leq R^2}$$ and $${\lambda_{i_{j}}-\lambda_{i_{1}}\in I_j}$$ for 2≤ j≤ l. We study the asymptotic behavior of $${K^{(l)}_I(R)}$$ as R tends to infinity. If k≥ 4 we prove $${K^{(l)}_I(R)\sim c_l(Q)\,{\rm vol}(I)R^{lk-2(l-1)}}$$ for arbitrary l, where c l (Q) is an explicitly determined constant. This remains true for k=3 under the restriction l≤ 3. Springer-Verlag, 2009 Diophantine inequalities nationallicence Quadratic forms nationallicence Correlation functions nationallicence Monatshefte für Mathematik Springer Vienna 162/1(2011-01-01), 69-88 0026-9255 162:1<69 2011 162 605 https://doi.org/10.1007/s00605-009-0161-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-009-0161-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Müller Wolfgang Institut für Statistik, Technische Universität Graz, 8010, Graz, Austria aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/1(2011-01-01), 69-88 0026-9255 162:1<69 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer